6 20 23 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 20   c = 23

Area: T = 55.31221822025
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 13.91553294643° = 13°54'55″ = 0.24328683157 rad
Angle ∠ B = β = 53.28656392638° = 53°17'8″ = 0.93300098492 rad
Angle ∠ C = γ = 112.7999031272° = 112°47'57″ = 1.96987144888 rad

Height: ha = 18.43773940675
Height: hb = 5.53112182202
Height: hc = 4.81097549741

Median: ma = 21.34224459704
Median: mb = 13.50992560861
Median: mc = 9.26601295887

Inradius: r = 2.25876400899
Circumradius: R = 12.47546479442

Vertex coordinates: A[23; 0] B[0; 0] C[3.58769565217; 4.81097549741]
Centroid: CG[8.86223188406; 1.6033251658]
Coordinates of the circumscribed circle: U[11.5; -4.83439260784]
Coordinates of the inscribed circle: I[4.5; 2.25876400899]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.0854670536° = 166°5'5″ = 0.24328683157 rad
∠ B' = β' = 126.7144360736° = 126°42'52″ = 0.93300098492 rad
∠ C' = γ' = 67.20109687281° = 67°12'3″ = 1.96987144888 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 6 ; ; b = 20 ; ; c = 23 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 6+20+23 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-6)(24.5-20)(24.5-23) } ; ; T = sqrt{ 3059.44 } = 55.31 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.31 }{ 6 } = 18.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.31 }{ 20 } = 5.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.31 }{ 23 } = 4.81 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6**2-20**2-23**2 }{ 2 * 20 * 23 } ) = 13° 54'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-6**2-23**2 }{ 2 * 6 * 23 } ) = 53° 17'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-6**2-20**2 }{ 2 * 20 * 6 } ) = 112° 47'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.31 }{ 24.5 } = 2.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 13° 54'55" } = 12.47 ; ;




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